Which transformation represents reflection across the Y-axis?

Which transformation represents reflection across the Y-axis?

• A. (x,y) = (x,y)
• B. (x,y) = (-x,y)
• C. (x,y) = (x,-y)
• D. (x,y) = (-y,-x)

Answer: (B)

Reflection across the Y-axis transforms each point in the coordinate plane by flipping it over the Y-axis. This means that for a point with coordinates (x, y), the x-coordinate changes its sign while the y-coordinate remains the same. In this case, when reflecting a point across the Y-axis, the new coordinates become (-x, y), which corresponds to option B. For example, a point at (3, 2) would be reflected to (-3, 2). The other transformations listed do not represent a reflection across the Y-axis: - The transformation represented by the first option leaves the points unchanged, which does not involve any reflection. - The third option changes the sign of the y-coordinate instead of the x-coordinate, which does not reflect the point across the Y-axis but rather reflects it over the X-axis. - The last option swaps the coordinates and negates both, resulting in a different type of transformation entirely, not a reflection across the Y-axis. Therefore, the transformation that accurately describes a reflection across the Y-axis is indeed represented by the second choice, where the x-coordinate negates while the y-coordinate remains constant.

Reflection across the Y-axis transforms each point in the coordinate plane by flipping it over the Y-axis. This means that for a point with coordinates (x, y), the x-coordinate changes its sign while the y-coordinate remains the same.

In this case, when reflecting a point across the Y-axis, the new coordinates become (-x, y), which corresponds to option B. For example, a point at (3, 2) would be reflected to (-3, 2).

The other transformations listed do not represent a reflection across the Y-axis:

• The transformation represented by the first option leaves the points unchanged, which does not involve any reflection.

• The third option changes the sign of the y-coordinate instead of the x-coordinate, which does not reflect the point across the Y-axis but rather reflects it over the X-axis.

• The last option swaps the coordinates and negates both, resulting in a different type of transformation entirely, not a reflection across the Y-axis.

Therefore, the transformation that accurately describes a reflection across the Y-axis is indeed represented by the second choice, where the x-coordinate negates while the y-coordinate remains constant.